OpenStax College Physics for AP® Courses, Chapter 23, Problem 4 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. The induced magnetic field inside this coil will try to oppose any change in magnetic flux through the coil. So first let's consider what direction the magnetic field created by this wire is and at the position of this coil, we use the right hand rule grabbing this wire with our right hand, thumb pointing up in the direction of current, our fingers curl in the direction of the magnetic field produced by this wire and it is into the page inside the coil. So in part (a), we are told that this current is increasing so that means there's more magnetic field strength going into the page and therefore more flux into the page so the induced field created by the current induced in this coil will oppose that increase into the page and it will do so by going in the opposite direction. So these blue dots represent magnetic field that is induced to oppose the increasing into the page and so the field is coming out of the page and to get a field out of the page inside this loop, we have to have the current going counter-clockwise because you can grab this loop with your right hand and your fingers will go up in the middle of the loop and we'll find that the thumb—if we are grabbing the top part of this coil— is pointing to the left and the thumb indicates the direction of the current and likewise on the bottom of the coil, if you grab it with your fingers pointing up inside the coil the thumb is pointing to the right. So the induced field opposes the increase in external field into the page by coming out of the page and the current will be counter-clockwise. Okay! (And then we can erase all that!) And part (b) says that the current in the wire decreases. So the current is in the same direction so the field is in the same direction— it's into the page in the coil— but now we are getting less field strength into the page due to the decreasing current in this wire. And so the induced field will try to replace what has been lost and so the induced field will be into the page to replace what's decreasing as a result of this decreasing current and so it has a field that's induced into the page the current must be going clockwise if you grab the bottom of this wire, fingers going into the page inside the loop, the thumb is pointing to the left and likewise same story if you grab the top of the loop there so this current is clockwise; the induced field replaces the external field in red that is diminishing that is going away because of the decreased current. Okay! And then part (c)... we are told that the current direction suddenly switches around. So initially, the field is into the page and then when the current switches, the field will be out of the page. So there's... the change in flux is caused by this change in the field direction and it's starting into the page and then coming out of the page— the induced field will try to oppose that— so the induced field is going to be into the page to replace what was their before... before we had a field into the page originally when the current was going up and the induced field will try to replace it now that it's changed to coming out of the page and so this will cause a current that is clockwise.